Probabilistic stratigraphic modelling from sparse boreholes based on deep learning

The safety and efficiency of geotechnical design and construction rely heavily on the stratigraphic model from site investigation. However, inherent intricate stratigraphic variations and sparse borehole data introduce uncertainty and pose challenges for subsurface stratigraphy modelling. This paper proposes a hybrid neural network of pixel bi-directional long short-term memory (bi-LSTM) with dense conditional random field for probabilistic stratigraphic modelling using limited site-specific boreholes. The proposed method provides a powerful and useful tool for effectively capturing complex spatial dependencies and probabilistic evaluation of subsurface stratigraphic uncertainty. Given the hierarchical and heterogeneous characteristics of layered soils, a novel soft-boundary label relaxation technique is developed to vectorize stratigraphic variables. Within the framework of the proposed hybrid neural network, the pixel bi-LSTM is combined with the Monte Carlo dropout to efficiently approximate complex stratigraphic distribution. By defining a linear combination of Gaussian kernels, the dense conditional random field is established in the predicted soil profile to further minimize uncertainty around stratigraphic boundaries. Furthermore, this model is illustrated by the synthetic case and applied to two real cases from Hong Kong. The proposed method can not only derive a more reasonable stratigraphic model but also map the spatial uncertainty.